“…The current article presents and analyzes the monotone iterative finite volume implicit-explicit scheme for the system with some monotonicity assumptions on đ, đ, described in the relevant sections. These kind of schemes (without the monotone iterative techniques) were studied in the literature for various physical systems, see, for example, Bispen et al [10] for Euler systems, Mudzimbabwe and Vulkov [11] for European Option Pricing, and Pareschi and Russo [12] for relaxation systems, to name a few. The strategy in these schemes is to divide the given system into two subsystems, consisting of the nonstiff and stiff operators, for which explicit and implicit time marching are used, respectively.…”